Dirty Neon, I'd like to add grime and age to a neon sign
You're on the right track. Using a texture to mix emission with diffuse would do something like that. A decal (image texture) would offer you more control, but you'd have to create it yourself (I only say "but" because I've never been very good at painting textures, and find it very intimidating, though others don't feel that way).

Another slightly different option is to use a texture to modify the emission color, or the emission strength of the emission shader itself (rather than mixing in a diffuse). I've tried this before with mixed results. The main problem I ran into was that the texture had to be very high contrast in order to make the change visible when the emission was as bright as it needed to be: as I set the emission brighter, the texture would just get washed out and became unnoticeable. When the contrast was high enough, I just got splotches of black instead of subtle, detailed cloudy texture. 

I suspect that you would have much better results if you were able to use a true HDRI image as the texture input for the strength value.

Incidentally, if you don't know already, it's very important for anyone using textures to understand the difference between the HDRI look and the HDRI format. The HDRI look looks neat, but the HDRI format actually contains orders of magnitude more data than conventional image formats. More info here. Yeah, this is kind of a pet campaign of mine ;-)